数据模型与决策运筹学课后习题和案例答案012.docx
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数据模型与决策运筹学课后习题和案例答案012.docx
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数据模型与决策运筹学课后习题和案例答案012
Chapter12
Decisionanalysis
ReviewQuestions
12.1-1Thedecisionalternativesaretodrillforoilortoselltheland.
12.1-2Theconsultinggeologistbelievesthatthereis1chancein4ofoilonthetractofland.
12.1-3Maxdoesnotputmuchfaithintheassessment.
12.1-4Adetailedseismicsurveyofthelandcouldbedonetoobtainmoreinformation.
12.1-5Thepossiblestatesofnaturearethepossibleoutcomesoftherandomfactorsthataffectthepayoffthatwouldbeobtainedfromadecisionalternative.
12.1-6Priorprobabilitiesaretheestimatedprobabilitiesofthestatesofnaturepriortoobtainingadditionalinformationthroughatestorsurvey.
12.1-7Thepayoffsarequantitativemeasuresoftheoutcomesfromadecisionalternativeandastateofnature.Payoffsaregenerallyexpressedinmonetaryterms.
12.2-1Themaximaxcriterionidentifiesthemaximumpayoffforeachdecisionalternativeandchoosesthedecisionalternativewiththemaximumofthesemaximumpayoffs.Themaximaxcriterionisfortheeternaloptimist.
12.2-2Themaximaxciterioncompletelyignoresthepriorprobabilitiesandignoresallpayoffsexceptforthelargestone.
12.2-3Themaximincriterionidentifiestheminimumpayoffforeachdecisionalternativeandchoosesthedecisionalternativewiththemaximumoftheseminimumpayoffs.Themaximincriterionisforthetotalpessimist.
12.2-4Themaximincriterionignoresthepriorprobabilitiesandignoresallpayoffsexceptthemaximinpayoff.
12.2-5Themaximumlikelihoodcriterionfocusesonthemostlikelystateofnature,theonewiththelargestpriorprobability.
12.2-6Criticismsofthemaximumlikelihoodcriterioninclude:
1)thiscriterionchoosesanalternativewithoutconsideringitspayoffsforstatesofnatureotherthanthemostlikelyone,2)foralternativesthatarenotchosen,thiscriterionignorestheirpayoffsforstatesofnatureotherthanthemostlikelyone,3)ifthedifferencesinthepayoffsforthemostlikelystateofnaturearemuchlessthanforanothersomewhatlikelystateofnature,thenitmightmakesensetofocusonthislatterstateofnatureinstead,and4)iftherearemanystatesofnatureandtheyarenearlyequallylikely,thentheprobabilitythatthemostlikelystateofnaturewillbethetrueoneisfairlylow.
12.2-7Bayes’decisionrulesaystochoosethealternativewiththelargestexpectedpayoff.
12.2-8Theexpectedpayoffiscalculatedbymultiplyingeachpayoffbythepriorprobabilityofthecorrespondingstateofnatureandthensummingtheseproducts.
12.2-9CriticismsofBayes’decisionruleinclude:
1)thereusuallyisconsiderableuncertaintyinvolvedinassigningvaluestopriorprobabilities,2)priorprobabilitiesinherentlyareatleastlargelysubjectiveinnature,whereassounddecisionmakingshouldbebasedonobjectivedataandprocedures,and3)byfocusingonaverageoutcomes,expectedpayoffsignoretheeffectthattheamountofvariabilityinthepossibleoutcomesshouldhaveonthedecisionmaking.
12.3-1Adecisiontreeisagraphicaldisplayoftheprogressionofdecisionsandrandomeventstobeconsidered.
12.3-2Adecisionnodeindicatesthatadecisionneedstobemadeatthatpointintheprocess.Aneventnodeindicatesthatarandomeventoccursatthatpoint.
12.3-3Decisionnodesarerepresentedbysquareswhilecirclesrepresenteventnodes.
12.4-1Sensitivityanalysismightbehelpfultostudytheeffectifsomeofthenumbersincludedinthemodelarenotcorrect.
12.4-2Itassuresthateachpieceofdataisinonlyoneplaceanditmakesiteasyforanyonetointerpretthemodel,eveniftheydon’tunderstandTreePlanordecisiontrees.
12.4-3Adatatabledisplaysresultsofselectedoutputcellsforvarioustrialvaluesofadatacell.
12.4-4Ifthereislessthana23.75%chanceofoil,theyshouldsell.Ifit’smore,theyshoulddrill.
12.5-1Perfectinformationmeansknowingforsurewhichstateofnatureisthetruestateofnature.
12.5-2Theexpectedpayoffwithperfectinformationiscalculatedbymultiplyingthemaximumpayoffforeachalternativebythepriorprobabilityofthecorrespondingstateofnature.
12.5-3Thedecisiontreeshouldbestartedwithachancenodewhosebranchesarethevariousstatesofnature.
12.5-4EVPI=EP(withperfectinformation)–EP(withoutmoreinformation)
12.5-5Ifthecostofobtainingmoreinformationismorethantheexpectedvalueofperfectinformationthenitisnotworthwhiletoobtainmoreinformation.
12.5-6Ifthecostofobtainingmoreinformationislessthantheexpectedvalueofperfectinformationthenitmightbeworthwhiletoobtainmoreinformation.
12.5-7IntheGoferbrokeproblemtheEVPI>Csoitmightbeworthwhiletodotheseismicsurvey.
12.6-1Posteriorprobabilitiesarerevisedprobabilitiesofthestatesofnatureafterdoingatestorsurveytoimprovethepriorprobabilities.
12.6-2Thepossiblefindingsarefavorablewithoilbeingfairlylikely,orunfavorablewithoilbeingquiteunlikely.
12.6-3Conditionalprobabilitiesneedtobeestimated.
12.6-4Thefivekindsofprobabilitiesconsideredareprior,conditional,joint,unconditional,andposterior.
12.6-5P(stateandfinding)=P(state)*P(finding|state).
12.6-6P(finding)=sumofP(stateandfinding)foreachstate.
12.6-7P(state|finding)=P(stateandfinding)/P(finding).
12.6-8Bayes’theoremisusedtocalculateposteriorprobabilities.
12.7-1Adecisiontreeprovidesagraphicaldisplayoftheprogressionofdecisionsandrandomeventsforaproblem.
12.7-2Adecisionneedstobemadeatadecisionnode.
12.7-3Arandomeventwilloccurataeventnode.
12.7-4Theprobabilitiesofrandomeventsandthepayoffsneedtobeinsertedbeforebeginninganalysis.
12.7-5Whenperformingtheanalysis,startattherightsideofthedecisiontreeandmoveleftonecolumnatatime.
12.7-6Foreacheventnode,calculateitsexpectedpayoffbymultiplyingthepayoffofeachbranchbytheprobabilityofthatbranchandthensummingtheseproducts.
12.7-7Foreachdecisionnode,comparetheexpectedpayoffsofitsbranchesandchoosethealternativewhosebranchhasthelargestexpectedpayoff.
12.8-1Consolidatethedataandresultsintoonesectionofthespreadsheet.
12.8-2Performingsensitivityanalysisonapieceofdatashouldrequirechangingavalueinonlyoneplaceonthespreadsheet.
12.8-3Adatatablecanconsiderchangesinonlyoneortwodatacells.
12.8-4One.
12.8-5Yes.Thespidergraphcanconsiderchangesinmanydatacellsatatime.
12.8-6SensIt’sspidergraphassumesthateachdatavaluevariesbythesameamount.Sensit’stornadodiagramovercomesthislimitation.
12.9-1Utilitiesareintendedtoreflectthetruevalueofanoutcometothedecision-maker.
12.9-2
12.9-3Undertheassumptionsofutilitytheory,thedecision-maker’sutilityfunctionformoneyhasthepropertythatthedecision-makerisindifferentbetweentwoalternativecoursesofactionifthetwoalternativeshavethesameexpectedutility.
12.9-4Thedecision-makerisofferedtwohypotheticalalternativesandaskedtoidentifythepointofindifferencebetweenthetwo.
12.9-5Thepointofindifferenceisthevalueofpwherethedecision-makerisindifferentbetweenthetwohypotheticalalternatives.
12.9-6Thevalueobtainedtoevaluateeachnodeofthetreeistheexpectedutility.
12.9-7Maxdecidedtodotheseismicsurveyandtoselliftheresultisunfavorableordrilliftheresultisfavorable.
12.10-1TheGoferbrokeproblemcontainedthesameelementsastypicalapplicationsofdecisionanalysisbutisoversimplified.
12.10-2Aninfluencediagramcomplementsthedecisiontreeforrepresentingandanalyzingdecisionanalysisproblems.
12.10-3Typicalparticipantsincludemanagement,ananalyst,andagroupfacilitator.
12.10-4Amanagercangotoamanagementconsultingfirmthatspecializesindecisionanalysis.
12.10-5Decisionanalysisiswidelyusedaroundtheworld.
Problems
12.1a)Max(A1)=6,Max(A2)=4,Max(A3)=8.Maximax=8withalternativeA3.
b)Min(A1)=2,Min(A2)=3,Min(A3)=1.Maximin=3withalternativeA2.
12.2a)Max(A1)=30,Max(A2)=31,Max(A3)=22,Max(A4)=29.Maximax=31withA2.
b)Min(A1)=20,Min(A2)=14,Min(A3)=22,Min(A4)=21.Maximin=22withA3.
12.3a)
StateofNature
Alternative
Sell10cases
Sell11cases
Sell12cases
Sell13cases
Buy10cases
$50
$50
$50
$50
Buy11cases
$47
$55
$55
$55
Buy12cases
$44
$52
$60
$60
Buy13cases
$41
$49
$57
$65
PriorProbability
0.2
0.4
0.3
0.1
b)Max(Buy10)=$50,Max(Buy11)=$55,Max(Buy12)=$60,Max(Buy13)=$65.
Maximax=$65withbuying13cases.
c)Min(Buy10)=$50,Min(Buy11)=$47,Min(Buy12)=$44,Min(Buy13)=$41.
Maximin=$50withbuying10cases.
d)Themostlikelystateofnatureistosell11cases.Underthisstate,sheshouldbuy11caseswithapayoffof$55.
e)
Jeanshouldbuy12cases.Themaximumexpectedpayoffis$53.60.
f)(i)0.2and0.5
Jeanshouldpurchase12cases.Themaximumexpectedpayoffis$55.20.
(ii)0.3and0.4
Jeanshouldpurchase12cases.Themaximumexpectedpayoffis$54.40.
(iii)0.5and0.2
Jeanshouldpurchase11cases.Themaximumexpectedpayoffis$53.40.
12.4a)Max(Conservative)=$30million
Max(Speculative)=$40million
Max(Countercyclical)=$15million
Maximax=$40millionwiththespeculativeinvestment
b)Min(Conservative)=–$10million
Min(Speculative)=–$30million
Min(Countercyclical)=–$10million
Maximin=–$10millionwitheithertheconservativeofcountercyclicalinvestment.
c)Thestableeconomyisthemostlikelystateofnature.
Thespeculativeinvestmenthasthemaximumpayoffforthisstate
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